Abstract
The graphs appear in many applications such as computer networks, data networks, and PERT networks, when the network includes a small number of devices, it can be drawn easily by hand, as the number of devices increases, drawing becomes a very difficult task. For this problem we will develop a new method for automatic graph drawing based on two steps, the first is applying the topology –shape –metric that is approaching to orthogonal drawings for the grid and the second step is applying the fuzzy genetic algorithm that is directed, in the topology –shape –metric the final drawing is achieved through three sequential steps: planarization, orthogonalization, and compaction. Each of these steps is responsible for the quality of the final drawing. Then the genetic algorithm applied at the planarization step of the topology-shape-metric to find the geometric position of each vertex to minimize bending in the graph. The developed technique generates a greater number of planar embedding by varying the order of edges’ insertion. This is achieved clearly in the Results given in the paper.
Highlights
The expanding use of computers into business, science and the home, making scientists tend to draw diagrams to understand computer software
The first step is the planarization step in this step reduces the number of edge crossings as much as possible
In 2001, Maurizio patrignani [4] presented study for the complexity of orthogonal compaction based on three problems consist of providing an orthogonal grid drawing, while minimizing the area, the total edge length, or the maximum edge length
Summary
The expanding use of computers into business, science and the home, making scientists tend to draw diagrams to understand computer software. In 1994, Di Battista [2] presented study to produce esthetically pleasing drawings of graphs based on main-cost-flow for both vertical and horizontal edge groups. In 1999 Klau, Petra Mutzel [3] presented an approach based on a branch – and – cut algorithm which computes optimally labeled orthogonal drawings for compaction and labeling problem. In 2007, D.Vrajitoru [11] applied a hybrid genetic algorithm to solve graph drawing problems. In this chapter we will use TSM to minimize the crossing in the graph and apply the FGA in the second step of TSM to find the geometric position of each vertex to minimize the bends in the graph to produce a graph with good esthetic criteria
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